We are continuing to invent, develop, and translate novel Magnetic Resonance (MR) based water displacement imaging methods from the bench to the bedside. Diffusion Tensor MRI (DT-MRI or DTI) is perhaps the best-known imaging method that we invented, developed, and successfully translated clinically. It measures a diffusion tensor of mobile water within tissues. The scalar parameters it produces are intrinsic properties of the tissue and, remarkably, we measure them without introducing contrast agents or dyes. One DTI-derived quantity, the orientationally-averaged diffusion coefficient (or mean ADC), has been the most successful imaging parameter developed to date to visualize an acute stroke in progress. Subsequently, we showed that DTI is effective in identifying Wallerian degeneration often associated with chronic stroke. Previous studies with kittens by Carlo Pierpaoli and colleagues showed DTI to be useful in following early developmental changes occurring in cortical gray and white matter, which are not detectable using other imaging methods. The development of a method to color-encode axon orientation in the brain by Sinisa Pajevic and Carlo Pierpaoli has allowed us to identify and differentiate anatomical white matter pathways that have similar structure and composition, but different spatial orientations. These Direction-Encoded Color (DEC) maps clearly show the main association, projection, and commissural white matter pathways in the human brain, and are a mainstay in modern Neuroradiology. They can even be seen in publications like Gray's Anatomy. To assess anatomical connectivity between different functional regions in the brain, we also proposed and demonstrated a way to use DTI data to trace out nerve fiber tract trajectories, for which we coined the term DTI tractography. This was made possible by the development and implementation of a general mathematical framework for obtaining a continuous, smooth approximation to the measured discrete, noisy, diffusion tensor field data by Sinisa Pajevic and Akram Aldroubi. Collectively, these methods and approaches have allowed us and many other groups around the world to perform detailed anatomical and structural analyses of the brain in vivo, which was only possible previously using laborious, invasive histological methods performed on excised tissue specimen. Our contributions to the invention and development of streamline tractography was an impetus for the creation of NIH's Human Connectome Project (HCP). As we began migrating DTI to large, multi-center and multi-patient studies, we began developing a battery of statistical techniques to interpret our imaging data quantitatively, specifically to be able to determine the statistical significance of differences observed in our data. To this end, we developed empirical Monte Carlo and Bootstrap methods for determining features of the statistical distribution of the diffusion tensor from real experimental DTI data. Another innovation was a novel tensor-variate Gaussian distribution that describes the variability of the diffusion tensor in an ideal DTI experiment, and can be used to optimize the design and efficiency of DTI experiments. More recently, we developed approaches to measure uncertainties of many tensor-derived quantities, including the direction of axonal pathways using perturbation and statistical approaches. These developments collectively provide the foundation for applying powerful hypothesis tests to address a wide array of important biological and clinical questions that previously could only be tackled in an ad hoc manner, if at all. More recently, we have been developing sophisticated mathematical/physical models of water diffusion profiles and related these to the MR signals that we measure, with the aim of using our MRI data to drill down into the voxel to infer new microstructural and architectural features of tissue (primarilyy white matter in the brain). One example of this is our composite hindered and restricted model of diffusion (CHARMED) MRI framework which provides a mean axon radius for a pack of axons, and an estimate of the intra and extracellular volume fractions. A more recent refinement of CHARMED, AxCaliber MRI, allows us to measure the axon diameter distribution (ADD) within an axon bundle as well from MR displacement imaging data. Sophisticated multiple pulsed field gradient (PFG) NMR and MRI sequences, developed by Michal Komlosh, and translated by Alexandru Avram, help us characterize microscopic anisotropy within tissues like gray matter that are macroscopically isotropic, appearing like a homogeneous gel in DTI. Dr. Komlosh and Ferenc Horkay have developed physical phantoms to test and interrogate mathematical models of water diffusion in complex tissues developed by Evren Ozarslan and Dan Benjamini. Evren also developed novel ways to interpret data obtained from the MR sequences to infer features of size, shape, and distribution of pores in biological tissue and other porous media. He also used the theory of fractals to characterize anomalous diffusion observed in various tissue specimen that are indicative of an underlying hierarchical organizational structure. Collectively, parameters derived from these novel measurements may provide new sources of MR contrast for promising neuroscience applications, such as in vivo (Brodmann or cytoarchitechtonic) parcellation of the cerebral cortex or clinical diagnostic applications, such as improved cancer detection or brain tumor staging. An important development has been a way to characterize non-Gaussian features of the displacement distribution measured using MRI. To this end, our group continues to work on reconstructing the average propagator (displacement distribution) and features derived from it, using a relatively small number of diffusion weighted images (DWI) to enable their clinical migration. The average propagator is the holy grail of displacement or diffusion imaging, which can by used to infer geometric features of microscopic restricted compartments as well as glean all of the information provided by DTI as well as other higher-order tensor (HOT) methods. One approach we used previously was an iterative reconstruction scheme along with a priori information and physical constraints to infer the average propagator from DWI data. Another approach was to use CT-like reconstruction method to estimate the displacement profile from DWI data. The most successful method to date, however, developed by Evren Ozarslan, uses special basis functions to represent the average propagator, which compresses the amount of DWI data required while providing a plethora of new imaging parameters or stains with which to characterize microstructural features in tissues. A direction our group has pursued more recently is inferring function from structure. This entails using our structural MRI data and inferring function or performance of large-scale brain networks. Alexandru Avram in our group has been developing many of these important applications. Collectively, these novel methods and methodologies represent a pathway to realizing in vivo MRI histology--providing detailed microstructural and microarchitectural information about cells and tissues that otherwise could only be obtained using laborious and invasive histological or pathological techniques applied on biopsied or excised specimens. They also form the core of what is now referred to as microstructure imaging. We continue to develop new ways to assess tissue structure and architecture in vivo and non-invasively, with the aim of translating these approaches to the clinic, and to the larger biomedical research community.